Measurements of gravity gradient are typically reported in units of eotvos, named after Prof. Lorand Eotvos, who made pioneering studies of the gradient of the earth's gravitational field. One eotvos is defined as a change in gravity of one tenth of a micro-g over a distance of one kilometer. That is, 1 eotvos=0.1 micro-g per kilometer=0.0001 micro-g per meter.
In the early 1970s, two methods were developed to measure gravity gradients. One method consists of a metallic sphere with high-density weights located at opposite ends of a diameter. The sensing sphere or floated torque-summing member is symmetric about this diameter. The sphere is suspended within the surrounding hollow sphere by a fluid, augmented by electrostatic suspension, such that the sensing sphere is free to rotate inside the surrounding sphere. When a given mass is passed by the device at an angle that is not perpendicular to the weighted diameter, the mass pulls more on the nearer weight than on the further. A torque is thereby exerted on the sensing sphere. The device includes a system that exerts a counter torque just sufficient to keep the sphere at a null position; the amount of counter torque is determined by a feedback system that is calibrated to a source of electric current. Because the moments of inertia of the sensing sphere are precisely known and the counter torque is measured, the components of the gradient of the gravitational field can be determined. This type of gravity gradiometer design was successfully built and tested. A typical response time of 1 minute for a signal of approximately 14 eotvos units was demonstrated with 0.25 eotvos accuracy through a measurement of gravity gradient produced by an 8.75 pound (4 kilogram) lead ball. A complete system of 3 gradiometers with gimbals, electronics, computers and power supply was estimated to be 230 kilograms in weight and projected to have an accuracy of 1 eotvos unit with a response time as short as 10 seconds. However, this proposed system was never built.
A second method employs pairs of diametrically opposed accelerometers mounted on a rotating table. The difference in quantities measured by the two opposing accelerometers is a measure of a component of gravity gradient in the plane of the disc. The difference signal between the two accelerometers is demodulated at twice the frequency of the rotation of the disc, yielding the required gravity gradient. This gravity gradiometer system, with improvements, represents the current state of the art. This system mechanization is referred to as “carouselling” and was initially used successfully for aircraft navigation systems.
Gravity gradiometers which incorporate multiple rotating accelerometers as their prime sensors use accelerometers which are based on torque-to-balance scientific principles but do not include a gyroscopic element. Fundamentally, these devices use a calibrated restraint to balance a pendulum. Their ultimate performance depends on the stability of a spring or the stability of the magnetic field of a torquer. Millions of dollars, spent over decades on materials and design refinements, have brought this torque-to-balance technology to its performance limit for this and similar applications. By rotating multiple torque-to-balance accelerometers, commercial systems are able to achieve the approximately two orders of magnitude performance improvement necessary to locate and discern minerals and hydrocarbon deposits. The performance is about 1 eotvos for static measurements on land, and about 5-7 eotvos for airborne measurements.